Fractional Calculus Lecture Notes

Fractional Calculus Lecture Notes

by Professor Francesco Mainardi

Also visit the CRUNCH group and the MURI Fractional PDE website

SERIES 1

Syllabus, Introduction to Fractional Calculus

Exercises on Fractional Calculus in IR+

Foundations of Fractional Calculus

The Eulerian Functions 

SERIES 2

Heisenbergs inequality for Fourier transform

Applications of the Fourier transform in the imaging analysis

Mittag-Leffler Functions Related Topics and Applications (cover)

Mittag-Leffler Functions, Related Topics and Applications (article)

An approach to the three sisters functions

Fractional Calculus and Waves in Linear Viscoelasticity

Essentials of Fractional Calculus

Essentials of Linear Viscoelasticity

Fractional Viscoelastic Models

Preface

On Some Properties of the Mittag-Leffler Function

SERIES 3

Abel Integral Equations:  An Introduction Via LaPlace Transform and Fractional Calculus

On Complete Monotonicity of the Prabhakar Function and Non-Debye Relaxation in Dielelctrics

Fractional Calculus and Special Functions

The Cycloid and the Tautochrone Problem

SERIES 4

Linear Diffusion Equation

The Two Forms of Fractional Relaxation of Distributed Order

Fractional Calculus:  Integral and Differential Equations of Fractional Order

Heisenberg's Inequality for Fourier Transform

SERIES 5

Higher Transcendental Functions

Salvatore Pincherle:  The Pioneer of the Mellin-Barnes Integrals

The Role of Salvatore Pincherle in the Development of Fractional Calculus

SERIES 6

Discrete random walk models for symmetric Levy-Feller Diffusion professes

The fundamental solution of the space-time fractional diffusion equation

Levy Stable Distributions in the Theory of Probability

Probability distributions generated by fractional diffusion equations

SERIES 7

Analytical Properties and Applications of the Wright Function

The Bessel Functions

The Wright Functions

SERIES 8

On the complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics

On Some Properties of the Mittage-Leffler Function...